Question: Simplify the following expression and state the condition under which the simplification is valid. $n = \dfrac{t^2 - 9}{t - 3}$
Answer: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = t$ $ b = \sqrt{9} = -3$ So we can rewrite the expression as: $n = \dfrac{({t} {-3})({t} + {3})} {t - 3} $ We can divide the numerator and denominator by $(t - 3)$ on condition that $t \neq 3$ Therefore $n = t + 3; t \neq 3$